Is diffraction affected by interaction between photons and electrons?

Question

Suppose we take a sheet of ordinary metal, make a narrow slit in it, and shine a light beam through the slit onto a screen. The light beam will diffract from the edges of the slit and spread out onto the screen.

Now let's take an identical sheet, with an identical slit, but this time made of neutronium, and shine an identical light through it.

Will the image on the screen be the same? Or are there additional interactions with the electrons in the first sheet which aren't present in the second experiment, and which cause the images to be different in the two experiments?

Answer 1

If the geometry of the sheets is the same, they will usually have very similar diffraction patterns. Textbook derivations of diffraction patterns only make use of the geometry; their equations do not involve, e.g. the dielectric constant of the material. They are using a simple model in which the only way light interacts with the material is that the material blocks it. This model is generally very accurate for the materials used in the experiment.

If you wanted a more refined picture, then the material could indeed affect the diffraction pattern. A simple example is to make the material transparent. Then the light would mostly pass right through, drastically altering the interference pattern.

Another drastic case would be if the photons were interacting incoherently with the material - e.g. flipping electron spins states. Then the electrons would contain "which path" information about the photons. This would destroy interference altogether.

Even neutrons can scatter photons, so there will always be at least some minor interaction, but the difference between diffraction from 1 micron slits in gold foil and a 1 micron slits in tin foil will probably be so slight as to be undetectable, simply because the interaction can be modeled well enough by saying that the slit itself is radiating coherently while the surrounding metal is not radiating at all.

If you really wanted to calculate the diffraction pattern accurately, you would need to account for the way light interacts with the metal in detail, but you would also need to account for the exact atomic structure of your slit and the exact shape of your wavefront and the exact density of the gas it's traveling through and the exact position of the screen you're observing on and the exact efficiency of your detectors, etc. My guess is that in most typical cases the error in being able to construct the geometry you want and to get a really pure wavefront dominates over the error due to the interactions of light with the material.

Finally, in x-ray diffraction, the material is not only important, but is the object of study. When we use light with wavelength of a few Angstroms to a few nanometers, we can see diffraction off of the atomic structure itself. The atoms become the "slits". This is a major source of our knowledge of the structure of crystals.

Answer 2

Generally, what causes diffraction patterns is the blocking or absorbing of some parts of a wavefront of light while allowing other parts to pass through unaltered. That in turn means that the exact nature of the material use to block some parts of the wavefront makes almost no difference in determining what kind of pattern will be formed. In particular -- and a bit counter-intuitively -- the edges of the material in a mask normally have almost no influence on the diffraction pattern produced.

The reason is that diffraction phenomena are wave phenomena, not particle effects. Unlike particles, waves always try to disperse. In fact, they are kept from dispersing almost entirely by the constructive interference effects of other nearby waves.

For example, if you pass light through a very small pinhole, the result is not at all like particles traveling through a hole. If it was, shining a bright light through a small pinhole would produce a sharp, tiny spot of light on the other side. Instead, you get light spreading out in all directions in a uniform, almost hemispherical pattern. If you have several such pinholes for a single distant source of light, you start seeing a really interesting effect: Interference patterns in which the light appears and disappears on the far side of the pinholes. These patterns reflect the geometry of the holes, where different distance cause the light waves to reinforce each other or destroy each other in different directions.

The more pinholes you add, the more complicated the patterns get -- and they can get very complicated indeed. A hologram is nothing more than an extraordinarily complex version of this effect of selectively passing and blocking sections of a wave front.

The reason we tend to think that light goes "straight" as its default path is very much an illusion. It happens because light has quite small wavelengths, compared to us, and a flashlight projects a very broad front of these waves. Even though such ordinary light is quite jumbled in terms of frequency and wave alignments (phase), the average result ends up being surprisingly well focused and able to project in a straight line.

A laser does even better. A laser uses one frequency with precise phase, and can produce wave fronts that "stick together" for absurdly long distances before they begin to fray out. Even more so than flashlights, lasers give the illusion that light naturally travels in straight lines, but it's really all smoke and mirrors (and even more so, waves).

So, to assess how light will react after going through any kind of mask that removes or blocks some parts of it and passes other parts of it, the trick is to assess the situation almost entirely in terms of wave theory: What kinds of waves are arriving? How orderly are they? And most importantly, exactly which parts of a wavefront are allowed to pass through, while the other parts are blocked?

It's a fascinating field with many important applications in modern life, from radio cell towers to lasers to the manufacture of silicon chips for electronics. All of these vital technologies depend on the specifics of how waves and wave diffraction patterns work.